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Largest Known Prime Number Found, And It’s A Whopping 22 Million Digits Long

By Shelley Hazen
Published on: 06:45 PST, Jan 20, 2016

A volunteer from Missouri has quite a track record for finding rare primes. For the fourth time, Curtis Cooper has “discovered” the largest prime number known to humankind.

In reality, a computer made all of the necessary calculations, but naturally, the human being behind that screen who notices the discovery gets the credit — and the $3,000 reward, BBC reported.

The figure is a real beast, and far beyond the comprehension of people with average mathematical prowess. And there is little value to the find other than that it’s fun, because no one can do anything with it.

“This prime is too large to currently be of practical value,” according to a statement announcing the discovery.

For a bit of a refresher, this kind of number can be divided only by themselves or one. For example: two, three, five, seven, and 13.

According to the Christian Science Monitor, primes are considered to be infinite, but they are harder to find the higher up you go.

And that’s why this discovery is such a big deal. Cooper — who is from the University of Central Missouri in Warrensburg — and his trusty machine had to count and calculate at unimaginable high numbers to find it, and already had a high bar to overcome.

The last largest known prime number was 17 million digits long, and was found on Jan. 25, 2013, New Scientist noted.

Because these rare digits are so long, they aren’t written out number by number, but as 2^74,207,281-1. This denotes two, multiplied by itself 74,207,280 times, with one subtracted afterwards. This prime, therefore, is a whopping 22 million digits long, or five million longer than the last one.

The previous record holder was 2 to the power of 57,885,161, minus 1.

So how exactly does a math enthusiast and his PC make this kind of discovery?

First of all, it was discovered through a global quest called the Great Internet Mersenne Prime Search, tasked with hunting the rarest of numbers. Abbreviated GIMPS, the huge project finds them by collaborating computing power online.

GIMPS is only interested in Mersenne primes, so named thanks to a math-lover and monk named Marin Mersenne, who studied them 350 years ago. They take the special form 2p-1. There are only 49 of them in the world, and GIMPS has found the last 15 in the 20 years it’s been going on.

It’s possible that the world has an infinite number yet to be discovered.

The computer tracks the largest known of these rare figures by multiplying two by itself continuously, then subtracting one. It goes through its paces automatically, testing the results to see if they’re prime (not all results are). Cooper’s found the largest known prime in September after 31 days of work, but in an odd twist, a bug prevented the software from sending out an email alert of the finding.

Routine maintenance months later finally unearthed it.

As you could guess, there’s little use for the largest known prime number, but they do have a distinct purpose: they exercise hardware and make sure it’s in tip top shape. A cybersecurity expert noted that the number-crunching can also help reveal problems with computer processes.

And they are important in computer encryption. Currently, primes in the hundreds of digits are used to ensure the security of online banking, shopping, private messaging, and other online activities.

So, in other words, thank you, two, three, five, seven, and 13, and so on…

[Photo by AlexanderZam/Shutterstock]

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